Problem: Hyun Woo is riding a ferris wheel. $H(t)$ models his height (in $\text{m}$ ) above the ground, $t$ seconds after the ride starts. Here, $t$ is entered in radians. $H(t) = -10\cos\left(\dfrac{2\pi}{150}t\right) + 10$ When does Hyun Woo first reach a height of $16\text{ m}$ ? Round your final answer to the nearest whole second.
Solution: Converting the problem into mathematical terms $H(t) = -10\cos\left({\dfrac{2\pi}{150}}t\right) + 10$ has a period of $\dfrac{2\pi}{{\scriptsize\dfrac{2\pi}{150}}}=150$ seconds. We want to find the first solution to the equation $H(t)=16$ within the period $0<t<150$. The answer The equation's two solutions within the desired period (rounded to the nearest whole second) are $53$ and $97$. Therefore, Hyun Woo first reaches a height of $16\text{ m}$ after about $53$ seconds.